a) Xét \(ΔDAH\) và \(ΔHAC\):
\(\widehat A:chung\)
\(\widehat{ADH}=\widehat{AHC}(=90°)\)
\(→ΔDAH\backsim ΔHAC(g.g)\)
b) \(HD⊥AC,AB⊥AC→HD//AB\)
\(→\dfrac{CH}{CB}=\dfrac{CD}{CA}\) (Định lý Talet) (1)
\(HI//OB\)
\(→\dfrac{IH}{OB}=\dfrac{CH}{CB}\) (Định lý Talet) (2)
\(ID//OA\)
\(→\dfrac{ID}{OA}=\dfrac{CD}{CA}\) (Định lý Talet) (3)
(1)(2)(3) \(→\dfrac{IH}{OB}=\dfrac{ID}{OA}\)
mà \(OB=OA\) (\(O\) là trung điểm \(AB\) )
\(→IH=ID\)
c) \(ΔDAH\backsim ΔHAC\)
\(→\dfrac{AD}{AH}=\dfrac{AH}{AC}\)
\(↔AH^2=AH.AC\) (4)
Xét \(ΔHBA\) và \(ΔHAC\):
\(\widehat{HBA}=\widehat{HAC}\) (cùng phụ \(\widehat C\) )
\(\widehat{BHA}=\widehat{AHC}(=90°)\)
\(→ΔHBA\backsim ΔHAC(g.g)\)
\(→\dfrac{BH}{AH}=\dfrac{AH}{CH}\)
\(↔AH^2=BH.CH\) (5)
(4)(5) \(→AD.AC=BH.CH\)
